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soldi70 [24.7K]
3 years ago
12

Triangle X Y Z is shown. The length of side X Y is (9 n + 12) feet and the length of side X Z is (15 n minus 6) feet. Angles X Y

Z and Y Z X are congruent. Consider isosceles ΔXYZ. What is the value of n? What is the measure of leg XY? ft What is the measure of leg XZ? ft
Mathematics
1 answer:
zmey [24]3 years ago
7 0

Answer:

n = 3

XY = 39

XZ = 39

Step-by-step explanation:

Given

XY = 9n + 12

XZ = 15n - 6

Solving (a): n

To solve for n;

We make use of

XY = XZ

Substitute values for XY and XZ

9n + 12 = 15n - 6

9n - 15n = -12 - 6

-6n = -18

Divide through by -6

n = 3

Solving (b) XY

XY = 9n + 12

Substitute 3 for n

XY = 9 * 3 + 12

XY = 27 + 12

XY = 39

Solving (c): XZ

XZ = XY

XZ = 39

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Given:

Compound shape

To find:

The area of the compound shape.

Solution:

The compound shape is splitted into two parallelograms.

<u>Bottom parallelogram:</u>

Base = 7.5 cm

Height = 5 cm

Area of the parallelogram = base × height

                                           = 7.5 × 5

                                           = 37.5 cm²

The area of the Bottom parallelogram 37.5 cm².

<u>Top parallelogram:</u>

Base = 7.5 cm

Height = 4.5 cm

Area of the parallelogram = base × height

                                           = 7.5 × 4.5

                                           = 33.75 cm²

The area of the top parallelogram 33.75 cm².

Compound shape = 37.5 + 33.75

                               = 71.25 cm²

The area of the compound shape is 71.25 cm².

7 0
3 years ago
Identify the pattern and find the next number in the pattern. 0.8, 3.2 12.851.2
Savatey [412]
For this case we have the following sequence:
 0.8
 3.2
 12.8
 51.2
 This sequence can be written as:
 0.8 = 0.2 * 4 = 0.2 * 4 ^ 1
 3.2 = 0.2 * 16 = 0.2 * 4 ^ 2
 12.8 = 0.2 * 64 = 0.2 * 4 ^ 3
 51.2 = 0.2 * 256 = 0.2 * 4 ^ 4
 Therefore, we have that the generic expression for this case is:
 an = 0.2 * 4 ^ n
 Then, the next number is then:
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8 0
3 years ago
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kipiarov [429]
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7 0
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Ghella [55]

Given is a piecewise function which follows different expressions according the the value of input x.

Given f(x)=\left \{ {{-10, \;if \;x2} } \right.

It says to find f(-4) i.e. the value of function f(x) at x = -4.

At point x = -4, f(x) is x³, if -5 ≤ x ≤ 2.

So, f(-4) = (-4)³

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4 0
3 years ago
1
Yakvenalex [24]

Answer:

Step-by-step explanation:

We know that the iceberg is 131 feet above the water and 273 feet bellow the water. We don't need the - on the 272 because we just want to know the length, no the direction it is going. so we add 131 and 272 and get 303.

3 0
3 years ago
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